Finite Group Databasebeta

← #11859122

Subgroups — #11859122

Order 1152.

849 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5522C211yesmaximal, characteristic
2#10592696C211yesmaximal, characteristic, complemented
3C3×#4997C211yesmaximal, characteristic, complemented
4#10591115C211yesmaximal, characteristic, complemented
5C2×Dic3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
6#10591071C211yesmaximal, characteristic
7#10591070C211yesmaximal, characteristic
8#10590265C212yesmaximal, complemented
9#10590264C212yesmaximal, complemented
10#10590262C212yesmaximal, complemented
11#10590261C212yesmaximal, complemented
12#82515—31nomaximal
13#78552—31nomaximal
14C2×C3×#235C2211yescharacteristic
15C32×#117C2211yescharacteristic
16C2×#3748C2211yescharacteristic
17C22×C3⋊(C3⋊C8)C2211yescharacteristic
18C2×C3×C4×Dic3C2211yescharacteristic
19C2×C3×#208C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21C3×#893C411yescharacteristic
22C3×#893C411yescharacteristic
23C3×#887C411yescharacteristic
24C3×#887C411yescharacteristic
25C3×#67⋊C4C412yes—
26C3×#67⋊C4C412yes—
27C3×#872C2212yes—
28C3×C42×D3C2212yes—
29#63630C2212yes—
30C4×C3⋊(C3⋊C8)C2212yes—
31C3×#803C2212yes—
32C3×C4×C3⋊C8C2212yes—
33Dic3⋊(C3⋊C8)C2211yescharacteristic
34Dic3⋊(C3⋊C8)C2212yes—
35Dic3⋊(C3⋊C8)C2211yescharacteristic
36Dic3⋊(C3⋊C8)C2211yescharacteristic
37Dic3⋊(C3⋊C8)C2212yes—
38Dic3⋊(C3⋊C8)C2211yescharacteristic
39(C2×D3)⋊(C3⋊C8)C2212yes—
40(C2×D3)⋊(C3⋊C8)C2212yes—
41(C2×D3)⋊(C3⋊C8)C2212yes—
42(C2×D3)⋊(C3⋊C8)C2212yes—
43C3×C4×#41—31no—
44#5522D311yescharacteristic
45C3×#405—31no—
46#5234—31no—
47#5234—31no—
48#5129—31no—
49#5118—31no—
50#5110—31no—
51C2×Dic3⋊C8—31no—
52#5000—32no—
53#5000—32no—
54#4997—31no—
55#4997—31no—
56#4997—61no—
57#4997D311yescharacteristic, complemented
58#4926—32no—
59#4925—32no—
60#4924—31no—
61C2×C4⋊(C3⋊C8)—31no—
62#4709—32no—
63#4705—32no—
64#4690—32no—
65#4685—32no—
66C22×C32×C4C2311yescharacteristic
67C2×C3×#67C2×C412yes—
68C22×C3×Dic3C2×C411yescharacteristic
69C22×C3×Dic3C2×C411yescharacteristic
70C3×#235—22no—
71C3×#235—22no—
72C2×C3×D12C2×C411yescharacteristic
73C2×C3×C4×D3C2×C412yes—
74C2×C3×C4×D3C2×C412yes—
75C2×C3×C4×D3C2312yes—
76C2×C3×Dic6C2×C411yescharacteristic
77C32×C4⋊C4C2×C411yescharacteristic
78C32×C4⋊C4C2×C411yescharacteristic
79C32×C22⋊C4C2×C412yes—
80C32×C42C2312yes—
81#3748—22no—
82C2×C3⋊(C3⋊C8)—22no—
83C2×C3⋊(C3⋊C8)C2311yescharacteristic
84C2×C3⋊(C3⋊C8)C2311yescharacteristic
85C2×C3⋊(C3⋊C8)C2312yes—
86C3×(C2×D3)⋊C4C2×C412yes—
87C3×(C2×D3)⋊C4C2×C412yes—
88C3×Dic3⋊C4C2×C412yes—
89C3×Dic3⋊C4C2×C412yes—
90C3×C4×Dic3C2×C412yes—
91C3×C4×Dic3C2×C412yes—
92C3×C4×Dic3C2×C411yescharacteristic
93C3×C4×Dic3C2×C411yescharacteristic
94C3×C4×Dic3C2311yescharacteristic
95C3×C4×Dic3C2311yescharacteristic
96C3×#208—22no—
97C2×C3×C3⋊C8—22no—
98C2×C3×C3⋊C8C2311yescharacteristic
99C2×C3×C3⋊C8C2311yescharacteristic
100C2×C3×C3⋊C8C2312yes—
101#2925—91noSylow
102C2×C3×#41—31no—
103C2×#235C2×D311yescharacteristic
104C2×C3×M16—31no—
105C22×C3×C8—31no—
106C3×C4×Q8—31no—
107C3×C4×Q8—31no—
108C3×C4×D4—31no—
109C3×C4×D4—31no—
110C3×C4×D4—32no—
111C3×C4×D4—32no—
112C3×#117—21no—
113C3×#117—32no—
114C3×#117C2×D311yescharacteristic
115C3×#117C2×D311yescharacteristic
116C2×C3×C42—31no—
117C2×C3×C42—32no—
118C2×C4×Dic3C2×D311yescharacteristic
119C2×#208—31no—
120C2×#208—31no—
121C2×#208—61no—
122C2×#208C2×D311yescharacteristic
123C22×C3⋊C8—31no—
124C22×C3⋊C8—31no—
125C22×C3⋊C8—61no—
126C22×C3⋊C8C2×D311yescharacteristic
127#893Dic311yescharacteristic
128#893Dic311yescharacteristic
129#887Dic311yescharacteristic
130#887Dic311yescharacteristic
131#67⋊C4Dic312yes—
132#67⋊C4Dic312yes—
133#872C2×D312yes—
134C42×D3C2×D312yes—
135C3×#97—32no—
136C3×C4×C8—32no—
137#830—32no—
138#830—32no—
139#830—32no—
140#830—32no—
141(C2×D3)⋊C8—32no—
142(C2×D3)⋊C8—32no—
143(C2×D3)⋊C8—32no—
144(C2×D3)⋊C8—32no—
145Dic3⋊C8—31no—
146Dic3⋊C8—32no—
147Dic3⋊C8—31no—
148Dic3⋊C8—32no—
149Dic3⋊C8—31no—
150Dic3⋊C8—31no—
151C4⋊(C3⋊C8)—31no—
152C4⋊(C3⋊C8)—31no—
153C4⋊(C3⋊C8)—31no—
154C4⋊(C3⋊C8)—31no—
155C4⋊(C3⋊C8)—32no—
156C4⋊(C3⋊C8)—32no—
157#803—32no—
158#803—32no—
159#803—62no—
160#803C2×D312yes—
161C4×C3⋊C8—32no—
162C4×C3⋊C8—32no—
163C4×C3⋊C8—62no—
164C4×C3⋊C8C2×D312yes—
165C23×C32C22×C411yescharacteristic
166C22×C3×D3C22×C412yes—
167C2×C32×C4C22×C412yes—
168C2×C32×C4C22×C412yes—
169C2×C32×C4C22×C411yescharacteristic
170C2×C32×C4#4112yes—
171C2×C32×C4#4112yes—
172C2×C32×C4C2411yescharacteristic
173C3×#67—24no—
174C2×C3×Dic3—22no—
175C2×C3×Dic3—41no—
176C2×C3×Dic3C22×C411yescharacteristic
177C2×C3×Dic3C22×C412yes—
178C2×C3×Dic3C22×C411yescharacteristic
179C2×C3×Dic3C22×C411yescharacteristic
180C2×C3×Dic3C22×C411yescharacteristic
181C3×D12—22no—
182C3×C4×D3—22no—
183C3×C4×D3—22no—
184C3×C4×D3—24no—
185C3×C4×D3—42no—
186C3×Dic6—22no—
187C3⋊(C3⋊C8)—21no—
188C3⋊(C3⋊C8)—21no—
189C3⋊(C3⋊C8)—22no—
190C3×C3⋊C8—21no—
191C3×C3⋊C8—21no—
192C3×C3⋊C8—22no—
193C4×#41—31no—
194#433—92no—
195#433—92no—
196#432—92no—
197#431—92no—
198#423—91no—
199C2×C4⋊C8—91no—
200#408—91no—
201#408—91no—
202#405—31no—
203#405—91no—
204C3×#41—62no—
205C3×#41—62no—
206C2×C3×Q8—31no—
207C2×C3×D4—32no—
208C2×C3×D4—31no—
209C22×C3×C4—21no—
210C22×C3×C4—31no—
211C22×C3×C4—31no—
212C22×C3×C4—32no—
213C22×C3×C4—32no—
214C22×C3×C4—32no—
215C22×C3×C4C22×D311yescharacteristic
216C22×C3×C4C22×D311yescharacteristic
217C2×#67C2×Dic312yes—
218C22×Dic3C2×Dic311yescharacteristic
219C22×Dic3C2×Dic311yescharacteristic
220#235—22no—
221#235—22no—
222C2×D12C2×Dic311yescharacteristic
223C2×C4×D3C2×Dic312yes—
224C2×C4×D3C2×Dic312yes—
225C2×C4×D3C22×D312yes—
226C2×Dic6C2×Dic311yescharacteristic
227C3×M16—62no—
228C2×C3×C8—31no—
229C2×C3×C8—32no—
230C2×C3×C8—31no—
231C2×C3×C8—62no—
232C3×C4⋊C4—21no—
233C3×C4⋊C4—21no—
234C3×C4⋊C4—32no—
235C3×C4⋊C4—32no—
236C3×C4⋊C4C4×D311yescharacteristic
237C3×C4⋊C4C4×D311yescharacteristic
238C3×C4⋊C4C2×Dic311yescharacteristic
239C3×C4⋊C4C2×Dic311yescharacteristic
240C3×C22⋊C4—22no—
241C3×C22⋊C4—32no—
242C3×C22⋊C4—32no—
243C3×C22⋊C4C4×D312yes—
244C3×C22⋊C4C2×Dic312yes—
245C3×C42—22no—
246C3×C42—31no—
247C3×C42—32no—
248C3×C42—31no—
249C3×C42—32no—
250C3×C42—31no—
251C3×C42—31no—
252C3×C42C22×D312yes—
253C3×C42C22×D312yes—
254(C2×D3)⋊C4C2×Dic312yes—
255(C2×D3)⋊C4C2×Dic312yes—
256Dic3⋊C4C2×Dic312yes—
257Dic3⋊C4C2×Dic312yes—
258C4×Dic3C2×Dic312yes—
259C4×Dic3C2×Dic312yes—
260C4×Dic3C2×Dic311yescharacteristic
261C4×Dic3C2×Dic311yescharacteristic
262C4×Dic3C22×D311yescharacteristic
263C4×Dic3C22×D311yescharacteristic
264#208—22no—
265#208—64no—
266#208—62no—
267#208—62no—
268C2×C3⋊C8—22no—
269C2×C3⋊C8—31no—
270C2×C3⋊C8—31no—
271C2×C3⋊C8—32no—
272C2×C3⋊C8—32no—
273C2×C3⋊C8—31no—
274C2×C3⋊C8—31no—
275C2×C3⋊C8—61no—
276C2×C3⋊C8—62no—
277C2×C3⋊C8—61no—
278C2×C3⋊C8—64no—
279C2×C3⋊C8—62no—
280C2×C3⋊C8—62no—
281C2×C3⋊C8C22×D311yescharacteristic
282C2×C3⋊C8C22×D312yes—
283C2×C3⋊C8C22×D311yescharacteristic
284C22×C32—21no—
285C22×C32—21no—
286C22×C32#11712yes—
287C22×C32C23×C411yescharacteristic
288C2×C3×D3—22no—
289C2×C3×D3—22no—
290C2×C3×D3—22no—
291C32×C4—22no—
292C32×C4—22no—
293C32×C4#11712yes—
294C32×C4C2×#4111yescharacteristic
295C32×C4C2×#4111yescharacteristic
296C3×Dic3—22no—
297C3×Dic3—21no—
298C3×Dic3—21no—
299C3×Dic3—21no—
300C3×Dic3#13112yes—
301C2×#41—31no—
302C2×M16—31no—
303C2×M16—91no—
304C22×C8—31no—
305C22×C8—91no—
306C4×Q8—31no—
307C4×Q8—31no—
308C4×D4—31no—
309C4×D4—31no—
310C4×D4—32no—
311C4×D4—32no—
312#117—32no—
313#117D3211yescharacteristic
314C2×C42—31no—
315C2×C42—32no—
316C4⋊C8—91no—
317C4⋊C8—91no—
318C4⋊C8—91no—
319C4⋊C8—91no—
320C4⋊C8—92no—
321C4⋊C8—92no—
322C22⋊C8—92no—
323C22⋊C8—92no—
324C22⋊C8—92no—
325C22⋊C8—92no—
326#97—32no—
327#97—92no—
328C4×C8—32no—
329C4×C8—92no—
330C23×C3—21no—
331C23×C3—32no—
332C23×C3C2×C4×D311yescharacteristic
333C23×C3C22×Dic311yescharacteristic
334C22×D3C22×Dic312yes—
335C3×Q8—62no—
336C3×D4—64no—
337C3×D4—62no—
338C2×C3×C4—21no—
339C2×C3×C4—22no—
340C2×C3×C4—22no—
341C2×C3×C4—21no—
342C2×C3×C4—22no—
343C2×C3×C4—22no—
344C2×C3×C4—31no—
345C2×C3×C4—31no—
346C2×C3×C4—31no—
347C2×C3×C4—31no—
348C2×C3×C4—32no—
349C2×C3×C4—64no—
350C2×C3×C4—62no—
351C2×C3×C4—62no—
352C2×C3×C4—62no—
353C2×C3×C4—122no—
354C2×C3×C4—121no—
355C2×C3×C4C2×C4×D312yes—
356C2×C3×C4C2×C4×D312yes—
357C2×C3×C4C2×C4×D311yescharacteristic
358C2×C3×C4#23512yes—
359C2×C3×C4#23512yes—
360C2×C3×C4#23512yes—
361C2×C3×C4#23512yes—
362C2×C3×C4C22×Dic312yes—
363C2×C3×C4C22×Dic312yes—
364C2×C3×C4C22×Dic311yescharacteristic
365C2×C3×C4C23×D311yescharacteristic
366C2×C3×C4C23×D311yescharacteristic
367#67—24no—
368C2×Dic3—22no—
369C2×Dic3—41no—
370C2×Dic3C22×Dic311yescharacteristic
371C2×Dic3C22×Dic312yes—
372C2×Dic3C22×Dic311yescharacteristic
373C2×Dic3C22×Dic311yescharacteristic
374C2×Dic3C22×Dic311yescharacteristic
375D12—22no—
376C4×D3—22no—
377C4×D3—22no—
378C4×D3—24no—
379C4×D3—42no—
380Dic6—22no—
381C3×C8—61no—
382C3×C8—61no—
383C3×C8—62no—
384C3⋊C8—21no—
385C3⋊C8—21no—
386C3⋊C8—22no—
387C3⋊C8—62no—
388C3⋊C8—62no—
389C3⋊C8—64no—
390C3⋊C8—61no—
391C3⋊C8—61no—
392C3⋊C8—61no—
393C3⋊C8—61no—
394C3⋊C8—62no—
395C3⋊C8—62no—
396C2×C32—22no—
397C2×C32C2×#11711yescharacteristic
398C2×C32C2×#13111yescharacteristic
399C2×C32#56811yescharacteristic
400C3×D3—42no—
401#41—62no—
402#41—62no—
403C2×Q8—31no—
404C2×D4—32no—
405C2×D4—31no—
406C22×C4—31no—
407C22×C4—31no—
408C22×C4—32no—
409C22×C4—32no—
410C22×C4—32no—
411C22×C4C2×D3211yescharacteristic
412M16—62no—
413M16—182no—
414C2×C8—31no—
415C2×C8—32no—
416C2×C8—31no—
417C2×C8—62no—
418C2×C8—91no—
419C2×C8—92no—
420C2×C8—91no—
421C2×C8—182no—
422C4⋊C4—32no—
423C4⋊C4—32no—
424C4⋊C4D3×Dic311yescharacteristic
425C4⋊C4D3×Dic311yescharacteristic
426C22⋊C4—32no—
427C22⋊C4—32no—
428C22⋊C4D3×Dic312yes—
429C42—31no—
430C42—31no—
431C42—31no—
432C42—32no—
433C42—31no—
434C42—32no—
435C42C2×D3212yes—
436C22×C3—21no—
437C22×C3—21no—
438C22×C3—21no—
439C22×C3—21no—
440C22×C3—21no—
441C22×C3—22no—
442C22×C3—41no—
443C22×C3—41no—
444C22×C3—62no—
445C22×C3—62no—
446C22×C3—62no—
447C22×C3#87212yes—
448C22×C3#92612yes—
449C22×C3C22×C4×D311yescharacteristic
450C22×C3C23×Dic311yescharacteristic
451C2×D3—22no—
452C2×D3—22no—
453C2×D3—22no—
454C3×C4—22no—
455C3×C4—22no—
456C3×C4—22no—
457C3×C4—22no—
458C3×C4—21no—
459C3×C4—21no—
460C3×C4—22no—
461C3×C4—32no—
462C3×C4—42no—
463C3×C4—42no—
464C3×C4—62no—
465C3×C4—61no—
466C3×C4—61no—
467C3×C4—61no—
468C3×C4#87212yes—
469C3×C4#92612yes—
470C3×C4C2×#23511yescharacteristic
471C3×C4C2×#23511yescharacteristic
472C3×C4C2×#23511yescharacteristic
473C3×C4C2×#23511yescharacteristic
474Dic3—22no—
475Dic3—21no—
476Dic3—21no—
477Dic3—21no—
478Dic3#94812yes—
479C32#292511yescharacteristic, complemented, Sylow
480C23—32no—
481C23C2×D3×Dic311yescharacteristic
482Q8—62no—
483D4—64no—
484D4—62no—
485C2×C4—31no—
486C2×C4—31no—
487C2×C4—31no—
488C2×C4—31no—
489C2×C4—32no—
490C2×C4—64no—
491C2×C4—62no—
492C2×C4—62no—
493C2×C4—62no—
494C2×C4—122no—
495C2×C4—121no—
496C2×C4#379812yes—
497C2×C4#379812yes—
498C2×C4C2×D3×Dic312yes—
499C2×C4C2×D3×Dic312yes—
500C2×C4C2×D3×Dic311yescharacteristic
501C2×C4C22×D3211yescharacteristic
502C8—61no—
503C8—61no—
504C8—62no—
505C8—181no—
506C8—181no—
507C8—182no—
508C2×C3—22no—
509C2×C3—22no—
510C2×C3—21no—
511C2×C3—21no—
512C2×C3—21no—
513C2×C3—42no—
514C2×C3—122no—
515C2×C3C2×#87211yescharacteristic
516C2×C3D3×#13111yescharacteristic
517C2×C3#575011yescharacteristic
518C2×C3C2×#92611yescharacteristic
519C2×C3C2×#94811yescharacteristic
520C2×C3#581911yescharacteristic
521D3—42no—
522C22—21no—
523C22—21no—
524C22—62no—
525C22—62no—
526C22—62no—
527C22#6385512yes—
528C22C22×D3×Dic311yescharacteristic
529C4—22no—
530C4—22no—
531C4—32no—
532C4—62no—
533C4—61no—
534C4—61no—
535C4—61no—
536C4#6385512yes—
537C4C2×#379811yescharacteristic
538C4C2×#379811yescharacteristic
539C3—21no—
540C3#7855211yescharacteristic, complemented
541C3#8251511yescharacteristic, complemented
542C2—22no—
543C2—122no—
544C2C2×#6385511yescharacteristic
545C2D3×#94811yescharacteristic
546C2#1059544111yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D32
commutator, socleC22×C32C23×C4
FittingC32×#117C22
prime radicalC2×C3×#235C22
cosocleC2×C32×C4C24
hypercenter#117D32
hypocenterC32#2925
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ #117

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #10592696C2semidirect
3. C3×#4997C2semidirect
4. #10591115C2semidirect
5. C2×Dic3⋊(C3⋊C8)C2semidirect
8. #10590265C2semidirect
9. #10590264C2semidirect
10. #10590262C2semidirect
11. #10590261C2semidirect
57. #4997D3semidirect
479. C32#2925semidirect
540. C3#78552semidirect
541. C3#82515semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C3×#55222
#105926962
C3×#49972
#105911152
C2×Dic3⋊(C3⋊C8)2
#105910712
#105910702
#105902652
#105902642
#105902622
#105902612
#825153
#785523